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Important Fabric parameters and Formulae

Cover FactorCover factor denotes the density of fabric i.e the area occupied by the threads in relation the air space between the threads.

Ratio of threads per inch to square root of count is defined as "cover factor" K. Cover factor determines the appearance,handle, feel, permiability, transparancy, limits of pick insertion and hardness of fabric. If p is spacing between threads in mils(1/1000 inch)
K = 1000/(p√C)
=29.3d1/(p√v)
where d1is diameter of thread in mils and specific volume of yarn is v. If v is assumed as 1.1
K = = 28 d1/p.
If count is in tex units, then cover factor is equal to threads per cm multiplied by square root of tex of yarn. When cover dactor is 28, d = p. The threads will contact at the point where they cross from one face to other phase of cloth. Higher cover factors can be obtained by compression of yarns or by distortion of structure.In practise, cover factor has to be kept lower than 28 to allow space for threads to pass over one another. . So very high values are possible only in one direction in which threads have high crimp. 28 is the limit for canvas. In poplins warp will have a higher cover factor than weft. Normal fabrics will have a cover factor of 12..

CrimpCrimp is defined as the proportion by which straightened length of yarn is higher than the cloth length which contains the yarn. For determining crimp a length of fabric,l is marked. Yarn is removed from marked length of fabric, straightened to remove the waves by application of tension and measuring its length(l1). Fractional Crimp, c = (l1 - l)/l. Tension applied to straighten the yarn is standardised at 16/C oz.

Weight per square yardWeight per square yard of fabric is equal to weight of warp and weft in a square yard of fabric.
Weight of warp = (K1(1+c1)0.6857)/√C1
Weight of weft = (K2(1+c2)0.6857)/√C2
Weight of one square yd of fabric = (K1(1+c1)0.6857)/√C1+ K2(1+c2)0.6857/√C2Weight per square yd of fabric = (1/√C1)0.6857{K1(1+c1) + K2(1 + c2) ß}
where suffices 1 and 2 refer to warp and weft and ß = √(C1/C2)

Crimp - spacing RelationshipBy neglecting bending resistance of yarn ,and assuming yarn cross section in fabric to be cicular Pierce(JTI 1937, T45) developed a geometrical model to determine crimp, thread spacing relationships. The lie of threads in a plain fabric under such conditions is shown in Fig 1.

Jammed structure with race course cross section
When warp or weft is jammed the threads get compressed and assume a cross section similar to that of an ellipse or race track. Race track cross section is more easily amenable to mathematical analysis.The lie of threads in jammed structure with race track cross section is shown in Fig 2.
Fig 2

From Fig it is seen that E =√(F2 -h2)where F = D1 + D2, the sum of warp and weft race track radii and A is width of race track and
p = E + (A - D)
√(F2 - h2) = p - (A - D) = q
h = √(F2 - q2)
√(1 - (q1/F)2) + √(1 - (q2/F)2) = 1. From this the maximum number of picks that can be inserted into a cloth for a given ends per inch and diameter of yarn can be determined and likewise for ends per inch.